The reasoning behind this idea, I think, is this: since the entire population depends on a search engine to do their work and pretty much everything else, search engines have become a utility and utilities should be state run.
Much in the same way railroads were nationalized in most of the EU sometime during the early 20th century or even earlier.
As far as railroads are concerned, it was probably a decent idea (not much free market competition possible there, really), but whether it works for a search engine remains to be seen.
Except that in a democracy, what a government controlled search engine does with your data is more transparent than what a publicly held company (Google, say) does with it.
Of course the EU itself is very far from being a democracy (unlike its member states) so I'm still not thrilled about the idea, but in principle I'm not opposed to it.
Much in the same way railroads were nationalized in most of the EU sometime during the early 20th century or even earlier.
As far as railroads are concerned, it was probably a decent idea (not much free market competition possible there, really), but whether it works for a search engine remains to be seen.